584 research outputs found
Implementation of homomorphic encryption technique
Fully homomorphic encryption has long been viewed as cryptography’s prized ”holy grail” amazingly helpful yet rather subtle. Starting from the breakthrough invention of FHE in 2009 by Craig Gentry, numerous schemes are presented then by various authors following the Gentry’s blueprint. We discuss the basic homomorphic encryption given by the DGHV over the integers. It is modification of the Gentry’s scheme which is based on the ideal lattices. The main idea of the DGHV scheme is its simplicity for the arithmetic operations. Our plan is to reduce the size of the public key which ultimately reduces the space complexity of the algorithm. We then further introduces the concept of the approximate common divisor problem on the DGHV scheme. We propose the GACD attack over the modulus switching and public key compression technique of DGHV scheme. The overall contribution of this work is analysis, design and performance of the scheme
Conditionals in Homomorphic Encryption and Machine Learning Applications
Homomorphic encryption aims at allowing computations on encrypted data
without decryption other than that of the final result. This could provide an
elegant solution to the issue of privacy preservation in data-based
applications, such as those using machine learning, but several open issues
hamper this plan. In this work we assess the possibility for homomorphic
encryption to fully implement its program without relying on other techniques,
such as multiparty computation (SMPC), which may be impossible in many use
cases (for instance due to the high level of communication required). We
proceed in two steps: i) on the basis of the structured program theorem
(Bohm-Jacopini theorem) we identify the relevant minimal set of operations
homomorphic encryption must be able to perform to implement any algorithm; and
ii) we analyse the possibility to solve -- and propose an implementation for --
the most fundamentally relevant issue as it emerges from our analysis, that is,
the implementation of conditionals (requiring comparison and selection/jump
operations). We show how this issue clashes with the fundamental requirements
of homomorphic encryption and could represent a drawback for its use as a
complete solution for privacy preservation in data-based applications, in
particular machine learning ones. Our approach for comparisons is novel and
entirely embedded in homomorphic encryption, while previous studies relied on
other techniques, such as SMPC, demanding high level of communication among
parties, and decryption of intermediate results from data-owners. Our protocol
is also provably safe (sharing the same safety as the homomorphic encryption
schemes), differently from other techniques such as
Order-Preserving/Revealing-Encryption (OPE/ORE).Comment: 14 pages, 1 figure, corrected typos, added introductory pedagogical
section on polynomial approximatio
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